A Comparative Analysis of DTM and HAM
Solutions for Hunter-Saxton Equation and
Fisher Equation

DibyenduSaha; SanjibSengupta

doi:https://doi.org/10.14445/22315373/IJMTT-V56P534

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 4 | Year 2018 | Article Id. IJMTT-V56P534 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P534

A Comparative Analysis of DTM and HAM Solutions for Hunter-Saxton Equation and Fisher Equation

DibyenduSaha, SanjibSengupta

Abstract

In this article, two partial differential equations (PDEs), namely Hunter-Saxton equation and Fisher equation, which are non-linear in nature and arise in different physical situations are adopted and their solutions compared by the differential transform method (DTM) and homotopy analysis method (HAM). The comparative analysis outlines the significant features and effectiveness of these methods to the nonlinear PDEs, as it is possible to find the closed form like approximate solutions with high degree of accuracy when compared to the exact solutions. Also, for the problems under consideration it has been observed that the HAM results better as compared to DTM. Beside both the methods discussed, can be extended to solve a class of problems arising in different practical situations.

Keywords

Nonlinear PDEs, Differential Transform Method (DTM), Homotopy Analysis Method (HAM), Hunter-Saxton Equation, Fisher Equation.

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Citation :

DibyenduSaha, SanjibSengupta, "A Comparative Analysis of DTM and HAM Solutions for Hunter-Saxton Equation and Fisher Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 4, pp. 236-243, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P534